Vector Bremsstrahlung by Ultrarelativistic Collisions in Higher Dimensions

A classical computation of vector bremsstrahlung in ultrarelativistic gravitational-force collisions of massive point particles is presented in an arbitrary number d of extra dimensions. Our method adapts the post-linear formalism of General Relativity to the multidimensional case. The total emitted energy, as well as its angular and frequency distribution and characteristic values, are discussed in detail. For an electromagnetic mediation propagated in the bulk, the emitted energy $E_{em}$ of scattering with impact parameter b has magnitude $E_{em} \sim e^4 e'^2 \gamma^{d+2}/(m^2 b^{3d+3})$, with dominant frequency $\omega_{em} \sim \gamma^2/b$. For the gravitational force the charge emits via vector field, propagated in the bulk, energy $E_{rad}\sim[G_D m' e]^2 \gamma^{d+2}/b^{3d+3}$ for $d \geq 2$, with dominant frequency $\omega\sim\gamma^2/b$ and energy $E_{rad}\sim[G_5 m' e]^2\gamma^{3}\ln \gamma/b^{6}$ for $d=1$, with most of the energy coming from a wide frequency region $\omega \in [\gamma/b),\gamma^2/b]$. For the UED model with extra space volume $V=(2\pi R)^d$ the emitted energy is $E_{UED}\sim (b^{d}/V)^2 E_{rad}$. Finally, for the ADD model, including four dimensions, the electromagnetic field living on 3-brane, loses on emission the energy $E_{ADD}\sim[G_D m'e]^2\gamma^{3}/(V b^{2d+3})$, with characteristic frequency $\omega_{ADD}\sim\gamma/b$. The contribution of the low frequency part of the radiation (soft photons) to the total radiated energy is shown to be negligible for all values of d. The domain of validity of the classical result is discussed. The result is analyzed from the viewpoint of the deWitt - Brehme - Hobbs equation (and corresponding equations in higher dimensions).Comment: 39 pages, 4 figure

Piercing of domain walls: new mechanism of gravitational radiation

Domain wall (DW) moving in media undergoes the friction force due to particle scattering. However certain particles are not scattered, but perforate the wall. As a result, the wall gets excited in the form of the branon wave, while the particle experiences an acceleration jump. This gives rise to generation of gravitational waves which we call "piercing gravitational radiation" (PGR). Though this effect is of higher order in the gravitational constant than the quadrupole radiation from the collapsing DWs, its amplitude is enhanced in the case of relativistic particles or photons because of absence of the velocity factor which is present in the quadrupole formula. We derive the spectral-angular distribution of PGR within the simplified model of the weakly gravitating particle-wall system in Minkowski space-time of arbitrary dimensions. Within this model the radiation amplitude is obtained analytically. The spectral-angular distribution of PGR in such an approach suffers from infrared and ultraviolet divergences as well as from collinear divergence in the case of a massless perforating particle. Different cut-off schemes appropriate in various dimensions are discussed. Our results are applicable both to cosmological DWs and to the braneworld models.Comment: 30 pages, 8 figure

Radiation reaction in curved space-time: local method

Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only {\em on the world-line}. We consider point particle interacting with scalar, vector (electromagnetic) and linearized gravitational fields in the (generally non-vacuum) curved space-time. To properly renormalize the self-action in the gravitational case, we use a manifestly reparameterization-invariant formulation of the theory. Scalar and vector divergences are shown to cancel for a certain ratio of the corresponding charges. We also report on a modest progress in extending the results for the gravitational radiation reaction to the case of non-vacuum background.Comment: 10 pages, ws-procs9x6, published in "Gravitation and Astrophysics", Proceedings of the VII Asia-Pacific International Conference National Central University, Taiwan 23 - 26 November 2005, ed. J.M. Nester, C.-M. Chen, J.-P. Hsu. World Scientific, 2006, pp. 345-35

The Group Methodology of Using Cloud Technologies in the Training of Future Computer Science Teachers

The development of cloud computing resources and their implementation in university education require an increase in the ICT-competence of future computer science teachers. The article considers the use of project method as an effective tool of encouraging students’ cooperation while solving practical problems and as a means of developing their essential professional skills. The following pedagogical approaches and techniques were used: partnership of group members, development of group work skills, heterogeneous grouping, combined use of individual and peer assessment, teacher’s monitoring of the students’ work, focus on the task and group work skills, chance for every member to be a leader, essential feedback. The authors suggest using private and public cloud technologies to support the implementation of group methodology in the teaching process. One of such technologies is academic cloud based on the Apache CloudStack platform. This cloud environment is deployed in Physics and Mathematics Department of Ternopil V. Hnatiuk National Pedagogical University. The suggested method has been verified experimentally by using Wilcoxon signed-rank test